Kerr effect

Kerr effect

Electrically induced birefringence that is proportional to the square of the electric field. When a substance (especially a liquid or a gas) is placed in an electric field, its molecules may become partly oriented. This renders the substance anisotropic and gives it birefringence, that is, the ability to refract light differently in two directions. This effect, which was discovered in 1875 by John Kerr, is called the electrooptical Kerr effect, or simply the Kerr effect.

When a liquid is placed in an electric field, it behaves optically like a uniaxial crystal with the optical axis parallel to the electric lines of force. The Kerr effect is usually observed by passing light between two capacitor plates inserted in a glass cell containing the liquid. Such a device is known as a Kerr cell or optical Kerr shutter. Light passing through the medium normal to the electric lines of force (that is, parallel to the capacitor plates) is split into two linearly polarized waves.

In certain crystals there may be an electrically induced birefringence that is proportional to the first power of the electric field. This is called the Pockels effect. In these crystals the Pockels effect usually overshadows the Kerr effect, which is nonetheless present. In crystals of cubic symmetry and in isotropic solids (such as glass) only the Kerr effect is present. SeeElectrooptics

Kerr Effect

the occurrence of double refraction in optically isotropic substances, such as liquids and gases, under the influence of a uniform electric field. It was discovered by J. Kerr in 1875. As a result of the Kerr effect, a gas or liquid in an electric field acquires the properties of a uniaxial crystal whose optical axis lies along the field.

To observe the Kerr effect, monochromatic light is passed through a polarizer (such as a Nicol prism) and is directed to a plane capacitor filled with an isotropic substance (a Kerr cell). The polarizer converts the naturally polarized light into linearly polarized light. If no voltage is applied across the capacitor plates, the polarization of the light passing through the substance remains unchanged, and the light is completely extinguished by the second Nicol prism, the analyzer, which is rotated through 90° with respect to the first prism. If a voltage is applied across the capacitor plates, the linearly polarized light wave in the substance is resolved into two waves, polarized along the field Ee (the extraordinary wave) and at right angles to the field Eo (the ordinary wave), which propagate at different speeds. Because of the difference in speed of propagation the oscillation phase of the electric vector for the extraordinary wave Ee and the ordinary wave E0 does not coincide. Because of this, the resultant light wave is elliptically polarized and passes partially through the analyzer. If a compensator that converts elliptically polarized light into linearly polarized light is placed between the Kerr cell and the analyzer, rotation of the compensator again makes possible complete extinguishing of the light by the analyzer. If the angle through which the compensator was rotated is known, it is possible to compute the magnitude of birefringence: Δn = ne – n0, where ne and n0 are the indexes of refraction for the extraordinary and ordinary waves.

The magnitude of birefringence is proportional to the square of the intensity of the electric field: Δn = nkE2 (the Kerr law), where n is the index of refraction of the substance in the absence of a field and k is the Kerr constant. The value B = nkλ is also called the Kerr constant (here λ is the wavelength of the light). The Kerr constants k and B may be positive or negative. Their magnitudes depend on the state of aggregation of the substance, on temperature, and on the molecular structure of the substance. For gases k~10-15 in cgs electrostatic units (esu). For liquids k~ 10-12 in cgs esu units. Still greater values of the Kerr constants are characteristic of rigid macromolecules and colloidal solutions.

An explanation of the Kerr effect was given by P. Langevin (1910) and M. Born (1918). An electric field tends to rotate the molecules of a substance in such a way that their dipole moment is directed along the field E. The electric field not only orients the molecules but also generates an additional dipole moment in the molecules. This is essential for inert gases, whose atoms have no dipole moment. The action of the field creates a definite orientation of the particles in the substance, and the conditions for propagation in the substance are different for waves polarized along and across the field. Thermal’motion hinders the orientation of atoms and molecules; therefore, the Kerr constant decreases with an increase in temperature. By measuring the Kerr constants it is possible to calculate the ellipsoid of optical polarizability, thus obtaining important information about molecular structure.

In an alternating electric field the Kerr effect depends on the speed of reorientation of the molecules upon a change in polarity of the field. This speed is very high for low-molecular-weight liquids (reorientation time < 10-9 sec). For this reason at electric field frequencies of less than 109 hertz, the intensity of light passing through the analyzer will follow the oscillations of the electric field (with doubled frequency) virtually without lag. Thus, a Kerr cell can operate as a modulator of a light flux; this fact is of great practical importance.

In addition to the electrooptical Kerr effect described above, a magnetooptical phenomenon was discovered by Kerr in 1876 (the magnetooptical Kerr effect) when observing the reflection of light from the polished surface of the pole of a magnet. In the magnetooptical Kerr effect, plane-polarized light reflected from a magnetized ferromagnetic material becomes elliptically polarized; concurrently, the major axis of the ellipsoid of polarization rotates through a certain angle with respect to the plane of polarization of the incident light. During observations of the magnetooptical Kerr effect the incident light must be polarized either in the plane of incidence or perpendicular to it, since any other polarization is complicated by the appearance of ellipticity of polarization caused by reflection from a metallic (nonmagnetized) surface.

The appearance of ellipticity of polarization and rotation of the plane of polarization is also observed when light passes through thin magnetized ferromagnetic films. Both magnetooptical effects are similar in nature and can be explained by the quantum theory. The magnetooptical Kerr effect is widely used in studying the domain structure of ferromagnetics.

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